Convert 14.7 pounds per square inch to Newtons per square meter: inch = 2.54 cm pound 4.45 N)
The Correct Answer and Explanation is:
To convert 14.7 pounds per square inch (psi) to Newtons per square meter (N/m²), we need to apply the given conversion factors:
- 1 inch = 2.54 cm
- 1 pound (lb) = 4.45 N
Step 1: Convert Pounds to Newtons
First, we know that 1 pound is equivalent to 4.45 Newtons. Therefore, 14.7 pounds can be converted to Newtons as follows:14.7 pounds×4.45 Nlb=65.415 N14.7 \, \text{pounds} \times 4.45 \, \frac{\text{N}}{\text{lb}} = 65.415 \, \text{N}14.7pounds×4.45lbN=65.415N
Step 2: Convert Inches to Meters
Next, we convert inches to meters. Since 1 inch equals 2.54 cm, and 1 cm equals 0.01 meters, we get the following:1 inch=2.54 cm=2.54×0.01 m=0.0254 m1 \, \text{inch} = 2.54 \, \text{cm} = 2.54 \times 0.01 \, \text{m} = 0.0254 \, \text{m}1inch=2.54cm=2.54×0.01m=0.0254m
So, 1 square inch is:1 in2=(0.0254 m)2=0.00064516 m21 \, \text{in}^2 = (0.0254 \, \text{m})^2 = 0.00064516 \, \text{m}^21in2=(0.0254m)2=0.00064516m2
Step 3: Convert Pounds per Square Inch to Newtons per Square Meter
Now that we have 14.7 pounds converted to 65.415 N and 1 square inch converted to 0.00064516 m², we can calculate the pressure in Newtons per square meter (also known as Pascals, Pa):65.415 N0.00064516 m2=101325 N/m2\frac{65.415 \, \text{N}}{0.00064516 \, \text{m}^2} = 101325 \, \text{N/m}^20.00064516m265.415N=101325N/m2
Thus, 14.7 psi is equivalent to 101,325 Newtons per square meter (N/m²).
Explanation:
Pressure is defined as force per unit area. In this case, we started with the unit of pressure in psi (pounds per square inch) and converted it step by step to the SI unit of pressure, which is Newtons per square meter (N/m²). We used known conversion factors for length and force (pounds to Newtons, and inches to meters) to make the necessary transformations. The final value, 101,325 N/m², corresponds to the standard atmospheric pressure at sea level, which is a well-known reference point in pressure measurements.
